Question: What do the following two equations represent? $3x-4y = 1$ $3x-4y = 5$
Explanation: Putting the first equation in $y = mx + b$ form gives: $3x-4y = 1$ $-4y = -3x+1$ $y = \dfrac{3}{4}x - \dfrac{1}{4}$ Putting the second equation in $y = mx + b$ form gives: $3x-4y = 5$ $-4y = -3x+5$ $y = \dfrac{3}{4}x - \dfrac{5}{4}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.